Patented 2,411,916 3,1946 ' ' ; UNITED STATES PATENT OFFICE MEASURING APPARATUS John R. 'Woodyard, Garden City, N; Y., assignor to Sperry Gyroscope Company, Inc., a corpora tion of New York Application June 28, 1943, Serial No. 492,573 11 Claims. (01. ‘172-245) 1 nating. quantities is modulated with the other to My invention relates to electrical measuring devices in general, and more particularly to meth ods and apparatus for determining the phase an; gle'between two alternating or periodically vary; ing quantities. ' produce a direct current proportional to a func tion of the ‘phase angle between them. ‘ The alternating quantities are recti?ed in an 5 other branch of the circuit by means of full-wave An object of my invention is to provide a de - recti?er-s and impressed on the signal and car- ' rier terminals of a second balanced modulator, the output of which is proportional to the product or the two periodically varying quantities.‘ The restoring force acting on the indicating element 10 outputs of each of the balanced modulators are thereof is independent of frequency. then delivered‘ to a quotient-taking device where Another object of myinvgention is to provide an the quotient of the two modulated outputs is electronic phase meter which is less affected by taken to give an indication of the phase angle to noise or other random ?uctuations than are .prior vice for measuring the phase difference between two periodically varying quantities in which the electronic phase meters. ' vbedetermined. - - . It is also ancbject of my invention to provide‘ 15 ' ' vA more comprehensive understanding of my in vention will be afforded from the following de a phase meter which utilizes the information of tailed description when taken together with the the impressed signal quantities over whole cycle periods. ' _ accompanying drawing in which, . _ Another purpose of my invention'is to provide a method and apparatus forv determining the 20 phase angle between two alternating electrical ' d Fig. 1 is a circuit diagram of‘ an embodiment of my invention; ' ' Fig. 2 is a modified block diagram of the cir- f quantitiesin which a product of the two is divided cuit shown inF-ig. 1; and by another product, obtained by multiplying the Fig. 31s a schematic diagram showing‘the op eration of the balanced modulators used in Fig. 1. two quantities after recti?cation, to give a meas urement of phase di?erence. , 25 - As indicated schematically in Fig. 2; the illus ' trated apparatus comprises a pair of balanced Another purpose of myv invention is to provide a phase meter in which no moving parts carry the quantities whose phase di?erence is to be modulators l3 and 80, each of which is made re sponsive .to both of‘ the vector voltages Eli and E2, which are to be compared in phase. The A still further object ‘of- my invention is to ar 30 modulator I3 is directly connected to the voltage range in an electronic phase-measuring circuit inputs E1 and E2 so as to yield an output propor two balanced modulators, which produce direct tional to the vector product of the input voltages, current outputs» respectively proportional to a which includes, the .phase angle factor, cos 0. On function of the phase angle between the two quan . the other hand, the balanced modulator 60 has .tities whose phase- di?erence is to be determined 35 recti?ers 3i and 43, respectively, interposed in and to their product, and a device such as a the inputconnections from the voltages E1 and crossed-coil ‘ohmmeter which is capable of tak E: so that phase-effect is eliminated and‘ 'D.-C. ing the quotient of the two direct currents so pro voltages representing scalar values E1 and E: are duced, to give an indication of the phase angle. Yet another purpose of my invention isto pro 40 supplied to the balanced modulator 60 rendering it responsiveto the scalar product of the volt vvide a method for determining the phase angle ages. The ratio instrument ‘His provided, which between two periodically varying electrical quan has input connections from the output of the. ele titles in which two direct currents are produced ments i3 and 60 for producing a phase angle '. therefrom by modulation and recti?catiodwhich measured. I ' are proportional to a function of the phase angle between the quantities and to their products, the quotient of the direct current quantities being 45 indication. , v , In the embodiment of my invention illustrated more in detail in Fig. 1, I provide two pairs of in put terminals“ and II which receive the alter~ 'nating quantities whose phase angles'are to be‘ Other objects of my invention will become a'p-' 50 compared. taken to give an indication of phase angle meas urement. , ._ ' From input terminals ll, the'quantity.v im parent and those listed more evident as the de scription proceeds. ' . . ' In practising my invention, in a preferred em bodiment thereof, Iprovide a circuit having two pressed thereon is conducted to transformer 14 whose tapped secondary forms the balanced cir cuit of balanced modulator i3; comprising the ' pairs of input terminals, each of which receives 55 electronic discharge devices i1 and I8, illustrated one of the two alternating quantities whose phase angle difference is to be measured. From these as triodes. input terminals the electrical quantities are de- - coupled in the cathode circuit of balanced modu-~ . ' Transformer IS; the secondary of which is lator l3, receives the electrical quantity impressed livered to the'signal and carrier input terminals of a balanced modulator where one of the ‘alter 60 upon input terminals I2.v Controlv grids i9 and 2,411,916 3 ' 24 of elements 11 and I8 receive signal voltages from the secondary winding of transformer 14 which are used to modulate the output of trans .former l5. The secondary of this transformer 15 is in series with energy source 16 and together 1 these elements form a circuit for connecting spective quantities are recti?ed to produce scalar quantities E1 and E2 which are delivered to bal anced modulator 60 operating as a product-tak ing circuit. The output of this last-mentioned circuit, proportional to the product ElEZ, and the current proportional to the product EIEZ cos 0, are cathodes 22 and 23 of elements 11 and 18 to the \mid-point of the secondary winding of trans former l4. _ 4 Within the recti?ers 3| and 43, each of the re delivered to a quotient-taking device 14 where division of the two quantities is made to give an _ Plates 2| and 25 of these elements deliver the 10 indication of 0. In operation, the balanced modulators l3 and, output of balanced modulator 13 to resistors 29 60 and the full-wave recti?ers 3| and 43 function and 30 and receive positive voltage from source normally and, accordingly, a detailed explanation 28. By-pass capacitors'26 and 21 are coupled in of their operation will not be made. A theoretical parallel with elements 11 and I8, respectively, for by-passing the alternating components of their 15 analysis of the operation of the balanced modu lator, with modulator l3 taken as an example, respective outputs. will be presented to explain the theory'of the The signal received on input terminals H is invention. \ also delivered to the primary winding of trans Referring to Fig. 3 and using the series expan former 32 which, together with the electronic discharge elements 33 and 34, comprises the full 20 sion for electrode currents, the plate current ii of tube 11 may be expressed as wave recti?er 3i. Anodes 35 and 31 of elements 33 and 34, both of which are illustrated as diodes, receive the output of the secondary winding of ‘and the plate current i2 of tube l8 as transformer 32 and their cathodes 36 and 38 deliver the output of the recti?er to a ?ltering 25 circuit comprising a resistor 39 and capacitors 4| Where the a’s are constants, the value of each de and 42. The output of full-wave recti?er 3| is pending upon tube characteristics and external delivered to the signal input terminals of balanced circuits, and ea and er are the instantaneous modulator 60, which in turn delivers it to the con trol grids 62 and 66 of elements 59 and 5!, com 30 values of signal and carrier voltages respectively, whose values may be expressedvas prising a part of balanced modulator 60. The electrical quantity received on the input (3) 8a==Ei sin wt terminals l2 passes through the primary winding and of transformer 44 and is induced in the secondary ‘ _ winding thereof for delivery to anodes 41 and 49 (4) 8b=E2 sin (wt-9) of elements 45 and 4B in the ‘full-wave recti?er where 6 is the phase angle between E1 and E2. 43. The output of this last-mentioned device is The resultant current ‘it delivered to terminals taken from cathodes 48 and 5| and delivered to 15 and 16 is therefore equal to the algebraic sum a ?ltering circuit comprising capacitor 52, resistor of the currents i1 and i: or 53, and capacitor 54. Through‘the ?ltering cir 40 (5) cuit last mentioned the output of the full-wave recti?er 43 is delivered to the balanced modulator which in terms of Equations ‘1 aid 2 may be 50 across the resistor 51. expressed as The output of balanced modulator 60, in the form of a direct current proportional to E1E2 is delivered from plates 63 and 61 of elements 59 ' By choosing the'proper operating voltages for the tubes 11 and i8, all components higher than the second order will be made negligible and and 5| to the resistors 12 and 13.‘ 'Plate current - is supplied the elements of balanced modulator 60 from source 1| and the grids thereof are biased from voltage source 58. By-pass capacitors 68 and 69 are coupled in the output circuit of bal anced modulator 60 for by-passlng .A. 0. com ' ponents. The direct current outputs of balanced modu lators I3 and 60 are delivered to a quotient-taking device 14, which is illustrated. as a crossed-coil ohmmeter and which is calibrated to give an in a1 dication of the phase angle existing between the two voltages impressed upon input terminals II and I2. - 60 While element 14 is illustrated as a crossed-coil ohmmeter it may take the form of any ratiometer or quotient-taking device, such as an Evershed “Meg'ger,” or may be of the electronic type in which electronic discharge-elements having log- . arithmic characteristic curves are used. With reference to Fig. 2, the operation of the circuit may be explained from a functional stand .point in the following manner: The vector quantity 1111 representing one of the ’ two alternating quantities, between which the phase angle difference is to be determined, is re ceived by balancedmodulator l3 where it modu lates the quantity 112 to produce a direct current output proportional to the quantity E1E2 cos 0. 75 Substituting the values of es and en, expressed by Equations 3 and 4, in Equation 8 and collect ing terms Since the alternating current components of the output current in of balanced modulator 13 are by-passed by capacitors 25 and 21, the direct current indc delivered to" terminals 15 and 16, as de?ned by the second term of Equation 9, is (10) iode=2d2E1E2 cos 0 and is proportional to EIEZ cos 0. ‘ 4 By similar analysis as evidenced by Equation 9 developed above, it is seen that the output iudc of balanced modulator 80 is proportional to the ‘ product EiEz, ‘and when combined by suitable means with the output of balanced modulator 2,411,910 6 ' . i3, expressed by Equation 10, a quantity pro trical quantities varying in phase with each other portional to cos 0 is obtained and through proper callbration may be indicated as the angle 0. Modi?cations in my invention are. of course, possible and may suggest themselves in ‘view of by an angle 0, means for producing from said al ternating electrical quantities a ?rst direct, cur rent proportional‘to a function of said angle 0, means for producing from said alternating elec trical quantities a second direct current propor tional to their-product, and means for taking the quotient of said ?rst and said second direct cur the foregoing disclosures. Accordingly, the spirit and-scope’of my invention is to be limited only by the appended claims. ' What is claimed is: ~ rents to give an indication of the value of said _ 1. Apparatus for determining the phase rela* -1D tionship between two periodically varying elec angle 0. / . . trical quantities, comprising means for modulat- ' 7. A method for measuring the phase diiference between two alternating electrical quantities, ing one of said quantities with the other, means comprising the steps of modulating one of said for rectifying each of said periodically varying ' quantities with the other to produce a-product quantities, means for modulating said recti?ed 15 thereof, converting each of said alternating electrical quantities into unidirectional quanti electrical quantities one with the other, and ties, combining said unidirectional quantities to means for receiving the outputs of the respective produce a product thereof, and combining both modulating means to give an indication of-phase. of said products so produced to give an indiy 2. In an electronic phase meter, a ?rst bal anced modulator for modulating one of two 20 cation of phase angle. 8. Av method of measuring the phase angle - periodically varying electrical quantities with ‘the other, separate recti?ers for rectifying each of .' ‘ between two periodically v'aryi'ngelectrical quan said periodically varying quantities, a second‘ . titles, comprising the stepsv of multiplying one » balanced modulator for modulating the output with the other to obtain a ?rst product, rectifying each of said periodically varying electrical quan titles to produce two unidirectional quantities, multiplying one of said unidirectional quantities of one of said recti?ers with'the output of the other, and means for determining the quotient _ of the outputs of said ?rst and second modulators , to give an indication of phase angle. ' 3. In an electronic phase meter a circuit having with the other to produce a second product, com bining said ?rst and second products to produce ) ‘.wo pairs of input terminals each of which re-. 30 an electrical quantity proportional to the phase angle between the two periodically varying elec ceive one of‘ two periodically varying electrical trical quantities, and measuring said last-men quantities, a balanced modulator for modulating. tioned electrical quantity to give an indication of one of said quantities with the other, first and *~ phase angle. 4 second full-wave rectifying‘ devices for rectifying 9. A method for determining the difference in each of said periodically varying electrical quan 35 phase between'two alternating electrical quanti tities, a balanced modulator-for modulating the ties, comprising the steps of modulating one of output of said ?rst full-wave recti?er with the said quantities with the other to produce a ?rst output of said second full-wave recti?er, and means including a crossed-coil ratiometer for re . modulated quantity, rectifying each of said alter ceiving the outputs of said balanced‘ modulators 40 nating electrical quantities to produce ?rst and . to give an indication of the phase angle between ' second recti?ed electrical quantities, modulating said ?rst recti?ed electrical quantity with said second recti?ed electrical quantity to produce a second modulated quantity, and taking the quo ‘ 4. Apparatus for measuring the phase relation ship between two periodically varying electrical v 45 tient of said ?rst and second modulated quanti ties to give an indication of phase angle. quantities, comprising means for taking the 10. A method for determining the phase angle product of said periodically varying electrical‘ quantities, means for rectifying each of said‘ ' between two periodically ‘varying electrical quan tities, comprising the steps of producing a ?rst periodically varying electrical quantities to pro . direct current from said periodically varying elec duc a plurality of recti?ed outputs, means for trical quantities proportional'to a function of the taking the product of said recti?ed outputs, and phase angle between them, producing a second means for dividing one product by the other to direct current from said periodically varying elec measure the phase angle between said periodically the two quantities impressed on the input terminals of the circuit. ' _ ' varying electrical quantities. ' . ' i ‘ trical quantities proportional to their product, 55 and taking the quotient of said ?rst and second direct currents to .give an indication of phase anced'modulator having'signal and carrier input ' 5. An electronic circuit comprising a ?rst hal .termlnals for respectively receiving ?rst and ' angle. ' . . 11. A method of measuring the phase relation ship between two periodically varying electrical separate means for rectifying said ?rst and second 60 quantities, comprising the'steps of modulating one of said periodically varying electrical quan periodically varying electrical quantities to pro titles with the other to produce a ?rst modulated duce corresponding ?rst and second recti?ed elec quantity, rectifying each of said periodically trical quantities, a second balanced modulator varying electrical quantities to produce two non for modulating said ?rst recti?ed electrical quan periodically varying electrical quantities there tity with said second recti?ed electrical quantity, from. modulating one of said non-periodically and means for dividing the output of said am varying electrical quantities with the other to , balanced modulator by that of said‘second bal second periodically varying electrical quantities differing in phase from each other by an angle 0, anced modulator to .give an indication of the produce a second modulated quantity, and com bining said first and second modulated quantities 6. An electronic phase determining device com 70 to give an indication of phase angle. angle 0. . prising means for receiving two alternating elec ' JOHN R. WOODYA‘RD.